A dice tower and/or dice box. The dice box is collapsible and becomes a case for dice. The dice tower can also fit inside the dice box case.
DiceBoxCase: A dice box that you roll your dice into so they don't roll off the table.
DiceBoxClasp: A clasp that holds the DiceBoxCase closed.
DiceTower: Put your dice into the hole at the top and your dice will exit at the bottom. The DiceTower will fit inside the DiceBoxCase.
The pictures show 9 dice being contained within the dice tower as the dice tower itself is contained within the dice box. To store the dice in the dice tower, hold it in your hand while blocking the exit, then place the dice in the top hole, largest first. You might be able to fit more depending on the size of your dice and the thickness of the felt you use (if any). If, like me, you have loads of dice, then consider printing more dice boxes to store them all.